What would happen if someone put together a list of every judge in the US and filed a lawsuit naming all of them as defendants? Obviously, it would be a frivolous lawsuit, but who can dismiss it without a conflict of interest? I don't think a jury trial is possible without an impartial judge?
It would be dismissed sua sponte on grounds including absolute judicial immunity from civil liability.
While conflict of interest rules for judges generally prohibit ruling on lawsuits in which you could potentially have an interest, there are narrow exceptions in cases where all judges are affected.
The Colorado Rule, which is similar in all U.S. jurisdictions, states:
In limited circumstances, the rule of necessity applies and allows judges to hear a case in which all other judges also would have a disqualifying interest or the case could not otherwise be heard.
Colo. Code. Jud. Cond. 2.11(D) ("Disqualification").